The invention presents the description of a new measurement based model that provides the basis for a theoretical description of the behavior of a power plant steam surface condenser performance under the influence of air in-leakage. The measurement is a quantification of properties of the water vapor and non-condensable gas mixture flowing in the vent line between the condenser and the exhauster. These properties are used, along with condenser measurements and operating conditions, to identify gas mixture properties inside the condenser. This model then is used to predict important condenser performance and behavior, which is compared to plant measurements and observations to confirm model validity. The measurement is shown to be compatible with requirements for modern power plant information systems supporting O & M, plant life, asset management and predictive maintenance. Innovative design modifications of present condenser systems and new systems and measurements are anticipated.
In 1963, Professor R. S. Silver (R. S. Silver, “An Approach to a General Theory of Surface Condensers”, Proceedings of the Institution of Mechanical Engineers, Vol. 178 Pt 1, No. 14, London, pp. 339-376, 1963-64) published a stimulating paper dealing with the general theory of surface condensers, wherein it was stated that, “It is well known to all operators and designers of condensing plants that the presence of a small proportion of air in the vapor can reduce the heat transfer performance in a marked manner.” In a recent publication by EPRI (R. E. Putman, Condenser In-Leakage Guideline, EPRI, TR-112819, January, 2000) on the effects of air ingress, it is stated, “ . . . but the presence of even small amounts of air or other non-condensables in the shell space can cause a significant reduction in the effective heat transfer coefficient.” In effect, for thirty-eight years, this understanding has remained entrenched and unchanged. In neither of these publications, nor any other publication or known paper, has a quantifiable amount of air in-leakage into an operating condenser resulted in a measured change in condenser performance that can be defined by a comprehensive theoretical treatment in support of these statements.
The currently accepted description of a condenser and the formulas for determining its performance are discussed below. The illustration in FIG. 1 represents the temperature profile of cooling water passing through tubes in a condenser. The following abbreviations apply to FIG. 1 and are used herein:                THW is the hotwell temperature, ° F.;        Tv is the vapor temperature, which can be set equal to the hotwell temperature THW, ° F.;        Tcw1 and Tcw2 are the inlet and outlet circulating water temperatures, respectively, ° F.;        TTD is the terminal temperature difference, ° F.;        ΔTcw is the rise in circulating water temperature, ° F.;        ΔTlm is the Grashof logarithmic mean temperature difference, which is the mean temperature driving force for heat flow between the exhaust steam vapor and cooling water in the condenser tubes, ° F.;        dt is the tube bundle density, tubes/ft3;        {dot over (m)}r is steam mass flow rate at r, lb/hr;        {dot over (m)}r,a is the steam & air mass flow rate at r, lb/hr;        {dot over (m)}t a is the steam mass flow rate per tube, lb/hr;        {dot over (m)}T a is the total steam mass flow rate, lb/hr;        na is the number of tubes in condenser;        na is the number of active tubes in condenser;        pa is the air partial pressure, “HgA;        pi is the partial pressure of ith gas, atmospheres;        po is the oxygen partial pressure, atmospheres;        ps is the steam partial pressure, “HgA;        PT is the condenser pressure, “HgA;        pv is the water vapor partial pressure, “HgA;        r is the radius in tube bundle, ft;        rs is the stagnant zone radius, ft;        vr is the steam velocity at radius r, ft/sec;        vr,a is the steam & air velocity at radius r, ft/sec;        AIL is the Air In-leakage, SCFM;        Hi is Henry's law constant for the ith gas, mole ratio/atmosphere;        L is the tube length, ft;        PPB is parts per billion, mole ratio;        R is the tube bundle diameter, ft;        SCF is standard cubic feet;        SCFM is standard cubic feet per minute; and        Ol is the solubility of the of the ith gas, mole ratio.The relationship between ΔTlm and other variables in FIG. 1 (in which all temperatures are in ° F.) is as follows:        
                              Δ          ⁢                                          ⁢                      T                          l              ⁢                                                          ⁢              m                                      =                                            T                              cw                ⁢                                                                  ⁢                2                                      -                          T                              cw                ⁢                                                                  ⁢                1                                                          ln            ⁡                          (                                                                    T                    v                                    -                                      T                                          cw                      ⁢                                                                                          ⁢                      1                                                                                                            T                    v                                    -                                      T                                          cw                      ⁢                                                                                          ⁢                      2                                                                                  )                                                          Eq        .                                  ⁢        1            Equation 1 in turn can be written as:
                              Δ          ⁢                                          ⁢                      T                          l              ⁢                                                          ⁢              m                                      =                              Δ            ⁢                                                  ⁢                          T              cw                                            ln            ⁡                          (                              1                +                                                      Δ                    ⁢                                                                                  ⁢                                          T                      cw                                                        TTD                                            )                                                          Eq        .                                  ⁢        2            Since ΔTcw is due to a steam load, Q (BTU/hr), from the turbine requiring energy removal sufficient to convert it to condensate, one also can write the following equations:Q={dot over (m)}cwcpΔTcw (Heat load to the circulating water)  Eq. 3and,Q={dot over (m)}shfg (Heat load from steam condensation)  Eq. 4where,
{dot over (m)}cw (lbs/hr) is the mass flow rate of circulating water,
cp (BTU/lb·° F.) the specific heat of water,
{dot over (m)}s (lbs/hr) the mass flow rate of steam, and
hfg (BTU/lb) the enthalpy change (latent heat of vaporization).
Combining Equations 3 and 4, yields the following equation:
                              Δ          ⁢                                          ⁢                      T            cw                          =                                                            m                .                            s                        ⁢                          h              fg                                                                          m                .                            cw                        ⁢                          c              p                                                          Eq        .                                  ⁢        5            which defines the rise in circulating water temperature in terms of mass ratio of steam flow to circulating water flow and two identifiable properties. Consistent with good engineering heat transfer practice in describing heat exchangers, Q is related to the exposed heat transfer surface area A, and ΔTlm, with a proportionality factor characteristically called the heat transfer coefficient, U. This relationship is given by:Q=UAΔTlm  Eq.6Combining equation (6) with equations (2) and (3), yields the following equation:
                                          m            .                    cw                =                  UA                                    c              p                        ⁢                          ln              ⁡                              (                                  1                  +                                                            Δ                      ⁢                                                                                          ⁢                                              T                        cw                                                              TTD                                                  )                                                                        Eq        .                                  ⁢        7            which, following rearrangement, becomes:
                    TTD        =                              Δ            ⁢                                                  ⁢                          T              cw                                            (                                          ⅇ                                  (                                      UA                                                                                            m                          .                                                cw                                            ⁢                                              c                        p                                                                              )                                            -              1                        )                                              Eq        .                                  ⁢        8            Since cp is constant, {dot over (m)}cw and ΔTcw held constant through a fixed load Q, and with A assumed constant, the terminal temperature difference becomes only a function of U, or:TTD=f(U)  Eq.9The theory goes on to say that the thermal resistance R, the inverse of U, can be described as the sum of all resistances in the path of heat flow from the steam to the circulating water, given by:
                    R        =                              1            U                    =                                    R              a                        +                          R              c                        +                          R              t                        +                          R              f                        +                          R              w                                                          Eq        .                                  ⁢        10            where,
a is air;
c is condensate on tubes;
t is tube;
f is fouling and
w is circulating water.
Historically, much effort has gone into analytically describing each of these series resistances. The best characterized are Rw, Rf, and Rt. Values of Rc, dealing with condensate on the tubes, have gained a lot of attention with some success; and Ra essentially has been ignored with the exception of near equilibrium diffusion limited experimental measurements and its associated theory (C. L. Henderson, et al., “Film Condensation in the Presence of a Non-Condensable Gas”, Journal of Heat Transfer, Vol. 91, pp. 447-450, August 1969). The latter generally is believed to be very complex (see Silver and Putman, supra) and limited data is available. The general belief is that small amounts of air will dramatically affect the heat transfer coefficient, resulting in an increase in the values of ΔTlm, TTD, and THW, without analytical description. The importance to the invention resides in part in that Ra is assumed to be treatable in a manner similar to tube fouling, as shown in Equation 10.